If you aim is to plot a discrete (but not necessarily arithmetic progression) you could use (where f here is x^2):

ListPlot[Table[x^2, {x, {1, 3}}]]

or use DiscretePlot:

DiscretePlot[x^2, {x, {1, 3}}]

A slightly simpler version of Issac Abraham's approach would be (using the function Map, see http://reference.wolfram.com/language/ref/Map.html)

ListPlot[f/@{1, 3, 8, 2.5}]

Issac's approach requires that the function that you use have the Attribute, Listable, which may often be the case for simple functions, but may not be true for more complicated ones. The approach that I gave does not depend on a Listable Attribute.